A. Ian and Array Sorting
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

To thank Ian, Mary gifted an array $$$a$$$ of length $$$n$$$ to Ian. To make himself look smart, he wants to make the array in non-decreasing order by doing the following finitely many times: he chooses two adjacent elements $$$a_i$$$ and $$$a_{i+1}$$$ ($$$1\le i\le n-1$$$), and increases both of them by $$$1$$$ or decreases both of them by $$$1$$$. Note that, the elements of the array can become negative.

As a smart person, you notice that, there are some arrays such that Ian cannot make it become non-decreasing order! Therefore, you decide to write a program to determine if it is possible to make the array in non-decreasing order.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of test cases follows.

The first line of each test case consists of a single integer $$$n$$$ ($$$2\le n\le 3\cdot10^5$$$) — the number of elements in the array.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le 10^9$$$) — the elements of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3\cdot10^5$$$.

Output

For each test case, output "YES" if there exists a sequence of operations which make the array non-decreasing, else output "NO".

You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).

Example
Input
5
3
1 3 2
2
2 1
4
1 3 5 7
4
2 1 4 3
5
5 4 3 2 1
Output
YES
NO
YES
NO
YES
Note

For the first test case, we can increase $$$a_2$$$ and $$$a_3$$$ both by $$$1$$$. The array is now $$$[1, 4, 3]$$$.

Then we can decrease $$$a_1$$$ and $$$a_2$$$ both by $$$1$$$. The array is now $$$[0, 3, 3]$$$, which is sorted in non-decreasing order. So the answer is "YES".

For the second test case, no matter how Ian perform the operations, $$$a_1$$$ will always be larger than $$$a_2$$$. So the answer is "NO" and Ian cannot pretend to be smart.

For the third test case, the array is already in non-decreasing order, so Ian does not need to do anything.